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Anticomplementary Conjugate

Suppose P=p:q:r and U=u:v:w are points, neither lying on a sideline of DeltaABC. Then the P-anticomplementary conjugate of U is the point

h(a,b,c,p,q,r,u,v,w):h(b,c,a,q,r,p,v,w,u):h(c,a,b,r,p,q,w,u,v),

where

h(a,b,c,p,q,r,u,v,w) =1/a[(b^2)/(q(au+cw))+(c^2)/(r(au+bv))-(a^2)/(p(bv+cw))].

If P is the incenter, then the P-anticomplementary conjugate is simply termed "the" anticomplementary conjugate.

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References

Kimberling, C. "Glossary: A Support Page for Encyclopedia of Triangle Centers." https://faculty.evansville.edu/ck6/encyclopedia/glossary.html.

Referenced on Wolfram|Alpha

Anticomplementary Conjugate

Cite this as:

Weisstein, Eric W. "Anticomplementary Conjugate." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AnticomplementaryConjugate.html

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